CN111082709A - Electric anti-backlash control method based on basal ganglia - Google Patents

Electric anti-backlash control method based on basal ganglia Download PDF

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CN111082709A
CN111082709A CN201911312275.8A CN201911312275A CN111082709A CN 111082709 A CN111082709 A CN 111082709A CN 201911312275 A CN201911312275 A CN 201911312275A CN 111082709 A CN111082709 A CN 111082709A
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basal ganglia
striatum
motor
globus pallidus
nucleus
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吴益飞
张通
郭健
陈庆伟
周唯
高俊宁
时锋
靳懿
吴红婷
吴鑫煜
刘洋
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Nanjing University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors

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Abstract

The invention discloses an electric anti-backlash control method based on basal ganglia, which is based on Izhikevich spike neurons, and basal ganglia synapses are constructed; constructing basal ganglia nuclei including striatum D1, striatum D2, globus pallidus ectonucleus, globus pallidus internus and subthalamic nucleus based on leaky-integrate neuron model; connecting basal ganglia nuclei by using basal ganglia synapses to construct a basal ganglia model; inputting the motor load current into the basal ganglia model, determining the importance of the motor bias voltage coefficient of each channel, selecting the motor bias voltage coefficient with the maximum importance to calculate the bias voltage of the motor, and finishing the electric backlash elimination control. The invention constructs the basal ganglia synapse based on the spike neuron model, and the bias voltage for controlling the electrical gap elimination of the system is more accurate.

Description

Electric anti-backlash control method based on basal ganglia
Technical Field
The invention relates to the field of motor control, in particular to an electric anti-backlash control method based on basal ganglia.
Background
Gear backlash is an indispensable problem for the normal operation of the mechanical transmission process, and is an important factor affecting the dynamic performance and steady-state accuracy of the system. The gear clearance elimination has two methods of mechanical clearance elimination and electric clearance elimination, and the control dynamic performance lag and the steady-state precision of the mechanical clearance elimination are not high, so the electric clearance elimination method is mostly adopted in industrial application. The traditional electric backlash eliminating method adds a fixed bias torque to a multi-motor servo system, but the fixed bias torque is easy to generate the phenomena of overlarge and too small bias force, so that the power consumption of the system is increased, and the output power of the multi-motor system is reduced.
Disclosure of Invention
The invention aims to provide an electric anti-backlash control method based on basal ganglia.
The technical solution for realizing the purpose of the invention is as follows: an electric anti-backlash control method based on basal ganglia comprises the following steps:
step 1, constructing a basal ganglia synapse based on an Izhikevich spike neuron;
step 2, constructing a basal ganglia nucleus based on a leaky integrate neuron model, wherein the basal ganglia nucleus comprises a striatum D1, a striatum D2, a globus pallidus ectonucleus, a globus pallidus internus and a subthalamic nucleus;
and 3, connecting the basal ganglia nuclei by using basal ganglia synapses to construct a basal ganglia model.
And 4, inputting the load current of the motor into the basal ganglia model, determining the importance of the motor bias voltage coefficient of each channel, selecting the motor bias voltage coefficient with the highest importance to calculate the bias voltage of the motor, and finishing the electric backlash elimination control.
Compared with the prior art, the invention has the following remarkable advantages: 1) constructing basal ganglia synapse based on the spike neuron model, wherein the connection strength of the synapse is more in line with the actual condition of motor operation; 2) in combination with models of synapses of basal ganglia and synapses of basal neurons, the bias voltage for the system electrical gap elimination is more accurate.
Drawings
Figure 1 is a schematic representation of a model of the basal ganglia of the present invention.
Figure 2 is a flow chart of the basal ganglia of the present invention.
Figure 3 is a graph of the coefficient of input bias voltage for the basal ganglia channel of the present invention.
Detailed Description
With reference to fig. 1, the method for controlling backlash of a double-motor system of a basal ganglia of the present invention comprises the following steps:
step 1, constructing a basal ganglia synapse based on an Izhikevich spike neuron;
the mathematical model expression of the Izhikevich spiking neuron model is as follows:
Figure BDA0002324847530000021
where v is the membrane potential of the Izhikevich spiking neuron, w is the intensity of the Izhikevich spiking neuron, and a, b are two recovery parameters of the model.
Adding motor load current excitation into a mathematical model of the Izhikevich spiking neuron model, and constructing a spiking neuron synapse mathematical model expression as follows:
Figure BDA0002324847530000022
in the formula IinThe neurons are excited by an external motor load current.
Step 2, constructing a basal ganglia nucleus based on a leaky integration neuron model;
the leaky-integration neuron model is:
Figure BDA0002324847530000023
wherein a is the state of the leaky-integrate neuron, u is the input of the leaky-integrate neuron, y is the output of the leaky-integrate neuron, k and m are proportionality coefficients, epsilon is the output threshold of the leaky-integrate neuron, and H is a step function.
Assuming that there are N channels in the basal ganglia, N groups of the same striatum D1, striatum D2, globus pallidus ectonucleus, globus pallidus internus and subthalamic nucleus need to be constructed, and each group of five types of nuclei is represented by a leaky-integrate neuron, and the mathematical model expression is as follows:
the mathematical model of the striatum D1 is:
Figure BDA0002324847530000024
in the formula ui SD1、ai SD1、yi SD1Respectively the input, state and output, ε, of the ith striatum D1SD1A threshold value is output for the striatum D1, and m and k are proportionality coefficients.
The mathematical model of the striatum D2 is:
Figure BDA0002324847530000031
in the formula ui SD2、ai SD2、yi SD2Respectively the input, state and output, ε, of the ith striatum D2SD2The output thresholds m, k for the striatum D2 are scaling factors.
The mathematical model of the globus pallidus outer nucleus is as follows:
Figure BDA0002324847530000032
in the formula ui GPe、ai GPe、yi GPeThe input, the state and the output of the ith globus pallidus ectonucleus are respectively, and m and k are proportionality coefficients.
The mathematical model of the globus pallidus kernel is as follows:
Figure BDA0002324847530000033
in the formula ui GPi、ai GPi、yi GPiRespectively the input, state and output of the ith globus pallidus kernel, ∈GPiIs the output threshold value of the globus pallidus kernel.
The mathematical model of the subthalamic nucleus is:
Figure BDA0002324847530000034
in the formula ui STN、ai STN、yi STNThe input, the state and the output of the ith globus pallidus ectonucleus are respectively, and m and k are proportionality coefficients.
And 3, connecting the nucleus masses of the cerebral cortex striatum D1, the striatum D2, the globus pallidus outer nucleus, the globus pallidus inner nucleus and the subthalamic nucleus of the basal ganglia by using the basal ganglia synapse to construct a basal ganglia model.
Motor bias voltage coefficient S of cerebral cortex to ith channeliThe following outputs are provided:
yi C＝Si
wherein i is the subscript of the channel, yi cI.e. the output representing the ith channel of the cerebral cortex.
Passing striatum D1 through wCSD1Connected to the ith channel of the cortex, striatum D2 passes through wCSD2Is connected with the ith channel of cerebral cortex, and the globus pallidus outer nucleus passes through wSD2GPeAnd wSTNGPeConnected to the striatum D2 and the subthalamic nucleus, which passes through wGPeSTNAnd wCSTNIs connected with globus pallidus ectonuclear and cerebral cortex, and globus pallidus kernelOver wSD1GPe、wSTNGPiAnd wGPeGPiAssociated with the striatal D1 nucleus, subthalamic nucleus, and pallidoluar nucleus. In the formula wCSD1、wCSD2、wSD2GPe、wSTNGPe、wGPeSTN、wCSTN、wSD1GPe、wSTNGPiAnd wGPeGPiThe synaptic strength w of the spiking neuron in step 1 represents its connection weight. Wherein wCSD1、wCSD2、wSD2GPe、wSTNGPeAnd wCSTNDenoted as excitation type, wGPeSTN、wSD1GPe、wSTNGPiAnd wGPeGPiIndicating an inhibition type.
According to the connection characteristics of the basal ganglia, the inputs of each group of striatum D1, striatum D2, globus pallidus outer nucleus, globus pallidus inner nucleus and subthalamic nucleus are:
Figure BDA0002324847530000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002324847530000042
input from the striatum D1, striatum D2, the globus pallidus outer nucleus, the globus pallidus inner nucleus and the subthalamic nucleus, respectively.
Figure BDA0002324847530000043
Is the output of the cerebral cortex, striatum D1, striatum D2, globus pallidus outer nucleus, globus pallidus inner nucleus and subthalamic nucleus. Y output from the globus pallidus kerneli GPiThe final output of the whole basal ganglia model represents the importance of the motor bias voltage coefficient of the ith channel and can be used for subsequent electric anti-backlash control.
And 4, determining the motor bias voltage coefficient of each channel according to the electric anti-backlash principle of multiple motors, inputting the motor load current into the basal ganglia model, determining the importance of the motor bias voltage coefficient of each channel, selecting the motor bias voltage coefficient with the highest importance, calculating the bias voltage of the motor, and finishing the electric anti-backlash control.
Fig. 3 shows a variation curve of the bias voltage coefficient, which is divided into three cases, corresponding to the motor bias voltage coefficient when the motor is overloaded, the motor is normally operated, and the motor is underloaded, specifically:
Figure BDA0002324847530000051
in the formula iset(x)Is the current of the x motor, y is the bias voltage coefficient input of the cerebral cortex, iabsTo select the maximum value of the input load current, the expression is:
iabs＝max(|i1|,…,|in|)
the input of the channel I is the overload bias voltage coefficient of the motor, the input of the channel II is the bias voltage coefficient of the normal operation of the motor, and the input of the channel III is the underload voltage coefficient of the motor.
Load current I of motorinAfter input, basal ganglia synapse with certain strength is formed, and the basal ganglia nucleus is connected with the basal ganglia synapse to obtain a basal ganglia model. The bias voltage coefficient of each channel is used as the input S of the cerebral cortexiAccording to the globus pallidus kernel output y of the basal gangliai GPiSelecting a channel with high importance as a final electric anti-backlash bias voltage coefficient, and determining a bias voltage expression for electric anti-backlash:
Uout＝Ubias·y
in the formula of UbiasIs rated power of the motor, UoutIs the bias voltage of the multiple motors.
The invention passes through the load current I of the motorinAnd determining model parameters of the basal ganglia, further determining the state of the motor, and selecting a corresponding bias voltage coefficient to complete electric anti-backlash control, so that the output power of synchronous working of multiple motors is ensured.

Claims (6)

1. An electric anti-backlash control method based on basal ganglia is characterized by comprising the following steps:
step 1, constructing a basal ganglia synapse based on an Izhikevich spike neuron;
step 2, constructing a basal ganglia nucleus based on a leaky integrate neuron model, wherein the basal ganglia nucleus comprises a striatum D1, a striatum D2, a globus pallidus ectonucleus, a globus pallidus internus and a subthalamic nucleus;
step 3, connecting basal ganglia nuclei by using basal ganglia synapses to construct a basal ganglia model;
and 4, inputting the load current of the motor into the basal ganglia model, determining the importance of the motor bias voltage coefficient of each channel, selecting the motor bias voltage coefficient with the highest importance to calculate the bias voltage of the motor, and finishing the electric backlash elimination control.
2. The method for controlling electrical backlash based on basal ganglia of claim 1, wherein in step 1, the specific method for constructing synapses of basal ganglia is as follows:
the mathematical model expression of the Izhikevich spiking neuron model is as follows:
Figure FDA0002324847520000011
wherein v is the membrane potential of the Izhikevich spiking neuron, w is the intensity of the Izhikevich spiking neuron, and a and b are two recovery parameters of the model;
adding motor load current excitation into a mathematical model of the Izhikevich spiking neuron model, and constructing a spiking neuron synapse mathematical model expression as follows:
Figure FDA0002324847520000012
in the formula IinThe neurons are excited by an external motor load current.
3. The basal ganglia-based electrical anti-backlash control method according to claim 1, wherein in step 2, the specific method for constructing basal ganglia nuclei is as follows:
the leaky-integration neuron model is:
Figure FDA0002324847520000013
wherein a is the state of the leaky-integrating neuron, u is the input of the leaky-integrating neuron, y is the output of the leaky-integrating neuron, k and m are proportionality coefficients, epsilon is the output threshold of the leaky-integrating neuron, and H is a step function;
if there are N channels in the basal ganglia, N groups of the same striatum D1, striatum D2, globus pallidus ectonucleus, globus pallidus internus and subthalamic nucleus need to be constructed, and each group of five types of nuclei is represented by a leaky-integrate neuron, and the mathematical model expression is as follows:
the mathematical model of the striatum D1 is:
Figure FDA0002324847520000021
in the formula ui SD1、ai SD1、yi SD1Respectively the input, state and output, ε, of the ith striatum D1SD1Outputting a threshold value for the striatum D1, wherein m and k are proportionality coefficients;
the mathematical model of the striatum D2 is:
Figure FDA0002324847520000022
in the formula ui SD2、ai SD2、yi SD2Respectively the input, state and output, ε, of the ith striatum D2SD2Outputting threshold values m and k for the striatum D2, wherein the threshold values m and k are proportionality coefficients;
the mathematical model of the globus pallidus outer nucleus is as follows:
in the formula ui GPe、ai GPe、yi GPeThe input, the state and the output of the ith globus pallidus outer nucleus are respectively, and m and k are proportionality coefficients;
the mathematical model of the globus pallidus kernel is as follows:
Figure FDA0002324847520000031
in the formula ui GPi、ai GPi、yi GPiRespectively the input, state and output of the ith globus pallidus kernel, ∈GPiIs the output threshold value of the globus pallidus kernel;
the mathematical model of the subthalamic nucleus is:
Figure FDA0002324847520000032
in the formula ui STN、ai STN、yi STNThe input, the state and the output of the ith globus pallidus ectonucleus are respectively, and m and k are proportionality coefficients.
4. The basal ganglia-based electrical anti-backlash control method according to claim 1, wherein in step 3, the specific method for constructing the basal ganglia model is as follows:
motor bias voltage coefficient S of cerebral cortex to ith channeliThe following outputs are provided:
yi C＝Si
wherein i is the subscript of the channel, yi cI.e. the output representing the ith channel of the cerebral cortex.
Passing striatum D1 through wCSD1Connected to the ith channel of the cortex, striatum D2 passes through wCSD2Is connected with the ith channel of cerebral cortex, and the globus pallidus outer nucleus passes through wSD2GPeAnd wSTNGPeConnected to the striatum D2 and the subthalamic nucleus, which passes through wGPeSTNAnd wCSTNConnected with globus pallidus ectonuclear and cerebral cortex, cangWhite sphere kernel pass wSD1GPe、wSTNGPiAnd wGPeGPiTo the striatal D1 nucleus, subthalamic nucleus and pallidotic nucleus, w in the above textCSD1、wCSD2、wSD2GPe、wSTNGPe、wGPeSTN、wCSTN、wSD1GPe、wSTNGPiAnd wGPeGPiIs a connection weight characterizing synaptic strength of the spiking neuron in step 1, related to the motor load current excitation corresponding to the neuron, where wCSD1、wCSD2、wSD2GPe、wSTNGPeAnd wCSTNDenoted as excitation type, wGPeSTN、wSD1GPe、wSTNGPiAnd wGPeGPiRepresents an inhibitory type;
according to the connection characteristics of the basal ganglia, the inputs obtained for each group of striatum D1, striatum D2, globus pallidus ectonucleus, globus pallidus internus and subthalamic nucleus are:
Figure FDA0002324847520000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002324847520000042
respectively input into striatum D1, striatum D2, globus pallidus outer nucleus, globus pallidus inner nucleus and subthalamic nucleus,
Figure FDA0002324847520000043
is the output of the cerebral cortex, striatum D1, striatum D2, globus pallidus outer nucleus, globus pallidus inner nucleus and subthalamic nucleus, wherein y is the output of the globus pallidus inner nucleusi GPiThe final output of the whole basal ganglia model represents the importance of the motor bias voltage coefficient of the ith channel and can be used for subsequent electric anti-backlash control.
5. The basal ganglia-based electrical backlash elimination control method according to claim 1, wherein in step 4, the motor bias voltage coefficient is divided into three channels, which respectively correspond to the conditions of motor overload, normal motor operation and motor underload, and specifically comprises:
Figure FDA0002324847520000044
in the formula iset(x)Is the current of the x motor, y is the bias voltage coefficient input of the cerebral cortex, iabsFor the maximum value of the input load current, the expression is:
iabs＝max(|i1|,…,|in|)。
6. the method for controlling electrical anti-backlash based on basal ganglia of claim 1, wherein in step 5, the channel with high importance is selected as the final electrical anti-backlash bias voltage coefficient, and multiplied by the rated power of the motor to obtain the bias voltage finally used for electrical anti-backlash.
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